Invented by Oliver Heaviside, a self-taught mathematician, physicist, and electrical engineer.
Denoted typically by a capital letter H.
Small letter h refers to a general function, not the Heaviside function.
Returns only two values: 0 or 1.
If the input value (x) is less than zero: returns 0.
If the input value (x) is equal to zero: returns 0.
If the input value (x) is greater than zero: returns 1.
Can be applied in various fields, including:
Laplace transformation.
Electrical devices (used to define on/off states).
Medical devices for monitoring body functions.
H(23) returns 1 (23 > 0).
H(0) returns 0.
H(-15.2) returns 0.
H(7.38) returns 1.
H(1.35) returns 1.
H(1) returns 1.
H(-1) returns 0.
H(-5) returns 0.
Remember to denote the Heaviside function properly; using a small h is incorrect.
In exam scenarios, problems may involve substituting x for specific values to find answers based on the Heaviside function.
For an exam question:
Replace x with 7: H(7) returns 1, with an additional answer to retrieve, such as 5/2.
Combine Heaviside function with other functions:
Signum() function and Identity function may be presented in problems.
Example: Signum(-25) = -1, H(3) = 1, Identity(-7) = -7. In the calculation: 9 - 1 - 1 = -2, and -7 + 9 = 2; thus the answer is -1.
The identity function is now introduced.
Further learning can be pursued through additional video resources.